SAT Question a67b9f88: Right Triangles And Trigonometry answer and explanation with Desmos solution

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs. The length of the hypotenuse of the right triangle shown is $53$. It’s given that $RS=\sqrt{105}$. Therefore, the length of one of the legs of the triangle shown is $\sqrt{105}$. Let $x$ represent $TS$, the length of the other leg of the triangle shown. Therefore, $53^2=(\sqrt{105}{)}^2+x^2$, or $2,809=105+x^2$. Subtracting $105$ from both sides of this equation yields $2,704=x^2$. Taking the positive square root of both sides of this equation yields $52=x$. Therefore, $TS$, the length of the other leg of the triangle shown, is $52$. The sine of an acute angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the hypotenuse. The length of the leg opposite angle $R$ is $52$, and the length of the hypotenuse is $53$. Therefore, the value of $\sin R$ is $\frac{52}{53}$. Note that 52/53, .9811, and 0.981 are examples of ways to enter a correct answer.